This is an application to evaluate a new set of statistical methods for testing gene-environment interactions (GxE) in the presence of gene-environment correlation in quantitative behavior genetic studies. Significance: Genes rarely influence health and mental health in isolation. Rather, genetic vulnerabilities are necessary but not always sufficient in the etiology of disorders because environmental factors often influence the expression of genetic vulnerabilities. Therefore, GxE is a critically important topic for all genetic research on health. The ultimate goal is to identify interactions between specific genetic polymorphisms and measured environments. Nonetheless, given the wide variety of possible environments involved in GxE for each phenotype, quantitative behavior genetic studies that infer latent genetic influences can serve as efficient screening tools for potential environmental modifiers of genetic influences, informing and strengthening subsequent molecular studies. Innovation: An influential paper by Purcell (2002) proposed a method for testing interactions between latent genetic influences and measured environments (GxM) in the presence of gene-measured environment correlation. We (Rathouz et al., 2008) recently examined statistical aspects of Purcell's approach and found that it incorrectly identifies GxM when it does not exist under some conditions. In addition, mathematical errors in Purcell's decomposition of the variance explained by genes and environments sometimes yield misleading conclusions. Because of the timely importance of accurately identifying GxM, robust statistical procedures must be available for testing it. We proposed a new class of such statistical models and showed how they can be compared to test for GxM (Rathouz et al., 2008). Approach: We request funding to evaluate our new models and procedures for testing GxM using simulation studies. We will develop publicly-available statistical software for fitting the models proposed in Rathouz et al (2008) that are not estimable in standard structural equation modeling software and we will establish sample sizes needed for adequate power under various conditions. We will evaluate the implications of Purcell's mathematically incorrect variance decomposition formulae when GxM is tested. In addition, we propose to evaluate and illustrate our new models in several tests of GxM in actual psychopathology data from two genetically informative data sets. An additional potentially serious concern with all models for testing GxM (Eaves, 2006) is that they are full probability structural models based on distributional assumptions such as the multivariate normality of latent genetic and environmental factors. Therefore, it is extremely important to know if our new GxM models are robust to violations of distributional assumptions or if they yield incorrect results when the scale of measurement of those variables is inherently non-normal. Therefore, we will conduct a series of simulation studies to examine the performance and robustness of our statistical models when distributional assumptions are violated, especially for the kinds of inherently skewed data that are typical in studies of psychopathology. PUBLIC HEALTH RELEVANCE: Gene-environment interactions (GxE) are profoundly important to the public health, but statistical methods for testing GxE in behavior genetic studies are just emerging. The requested funds will allow us to solve important problems in existing statistical methods and evaluate new methods that are more flexible and robust.